Question: Solve for $x$ and $y$ using elimination. ${-4x+y = -20}$ ${-3x-y = -29}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $-7x = -49$ $\dfrac{-7x}{{-7}} = \dfrac{-49}{{-7}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {-4x+y = -20}\thinspace$ to find $y$ ${-4}{(7)}{ + y = -20}$ $-28+y = -20$ $-28{+28} + y = -20{+28}$ ${y = 8}$ You can also plug ${x = 7}$ into $\thinspace {-3x-y = -29}\thinspace$ and get the same answer for $y$ : ${-3}{(7)}{ - y = -29}$ ${y = 8}$